Controllability of systems of interconnected membranes
type: Item
instance of: scholarly article
title: Controllability of systems of interconnected membranes
zbMATH Open document ID: 0901.73059
author: John E. Lagnese
published in: Discrete and Continuous Dynamical Systems
publication date: 1998-12-02T00:00:00Z
review text: The author considers the problems of approximate and exact controllability of the transient behavior of a system of interconnected, two-dimensional elastic membranes in three-dimensional space. The membranes can have different material properties. Control inputs and outputs are assumed to be restricted to the outer edges of the network and to the junction regions, where two or more membranes are joined. The object is to characterize those membrane configurations which are approximately, or exactly, controllable. A class of membrane configurations which may be approximately controlled from the outer edges alone is identified. The main result: Any two-membrane network may be approximately controlled from an arbitrarily small open subset of the outer boundary of one of the membranes. Moreover, it is proved that, under some restrictions on the geometries of the individual membranes and the overall configuration, exact controllability can be achieved through the action of controls along both the outer boundaries and in the junction regions of the network.
Mathematics Subject Classification ID: 74M05
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1010956
zbMATH Keywords: linear partial differential equations
zbMATH Keywords: exact controllability
zbMATH Keywords: approximate controllability
zbMATH Keywords: two-membrane network
zbMATH Keywords: small open subset
zbMATH Keywords: junction regions
reviewed by: Jan Lovíšek
MaRDI profile type: Publication
full work available at URL: dcds.1995.1.17
OpenAlex ID: W2085628645
DOI: 10.3934/DCDS.1995.1.17
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description: scientific article; zbMATH DE number 1010956